Property Posters

Group Size:Small Groups

Summary:This activity is going to focus on helping students remember
the commutative, associative, distributive, and identity properties
of addition and multiplication by having the students create posters
that they will hang around the school or classroom.

Materials:Invitation to Learn

Examples of different
types of posters
(movie, educational,
motivational, sport, or
quick reference)

Math journals

Instructional Procedures

Poster Paper

Crayons

Math Journals

Background For Teachers:The most important background information for this activity is
that teachers need to be familiar with the commutative and associative
properties of addition and multiplication. They also need to be familiar
with the zero and identity properties of multiplication and know how
to teach these properties to their students.

The commutative property is the one that refers to moving numbers around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.

The identity property teaches us that any number multiplied by 1 will always equal
that same number.

Finally, the zero property of multiplication teaches
us that any number multiplied by 0 will always equal 0.

4. Communicate mathematical ideas and arguments coherently to peers,
teachers, and others using the precise language and notations of mathematics.

Instructional Procedures:Invitation to Learn

The purpose of this invitation to learn is to help students
understand that posters are used for a variety of reasons, many
of which focus on advertising, communication, and information.
Before beginning this activity, place a variety of posters around the
room. Most classrooms already have posters hanging in them but
for this activity try and hang some new or different posters that are
new to the students.

Begin by saying, “As you may have noticed, I have hung some
different posters around the room. I want you to take a few minutes,
wander around the room, and look at the posters. As you wander, I
want you think about the questions I am going to write on the board.”
Write the following questions on the board: Why do we have posters
(what do posters do)? Are there different types of posters? Which
ones do you like the best?

Then say, “The questions I want you to think about are: Why
do we have posters (what do posters do)? Are there different types
of posters? And which ones do you like the best? After you have
wandered around the room, I want you to take a minute or two and
write down your thoughts in your math journals.” Give the students
two or three minutes to look at the posters before sending them back
to their desks to write in their journals.

After the students have written in their math journals, start with
question one and say, “Let’s talk about why we have posters. Does
anyone have any ideas about why we have posters?” Let the students
share their ideas. Help them come to the understanding that posters
are used to advertise things, communicate ideas, entertain, and share
information.

Then ask, “How many of you think that there are different types of
posters? Do we have different types of posters in our classroom?” Call
on different students to point at different posters throughout the room.
As you point them out, compare different posters, finding similarities
and differences.

End this invitation to learn by discussing the third question. Say,
“So, which posters did you like the best?” As you call on students to
share, follow up this question with the famous “Why?” It is important
that students explain why they like the posters. This will help them as
they design their own posters in the next activity.

Instructional Procedures

This activity is going to focus on helping students remember
the commutative, associative, distributive, and identity properties
of addition and multiplication by having the students create posters
that they will hang around the school or classroom. However,
this activity is not going to focus on teaching the properties. If
the students haven't written these properties down in their math
journals yet, have them write them down as you review.

Begin this activity by dividing your class into groups of 4-6
students. Start by saying, “Today we are going to be reviewing
the properties of addition and multiplication. When we are
done, we are going to make posters that we can place around
the room or school to help us remember them.”

Go to the board and write Properties of Addition and
Multiplication. Say, “There are four properties that we are
going to include on our posters. I am going to model and
review the properties first, and then you will get into your
groups and design a poster that demonstrates each property.”

Next say, “We are going to start with the commutative property.
The Commutative property teaches us that when we add or
multiply two numbers, we can add or multiply them in any
order.”

Write 2 + 4 and 2 x 4 on the board. Start with 2 + 4 and say,
“Let’s look at 2 + 4. When we add 2 and 4 together, what do
we get? 6.” Now ask, “What happens when I switch the 4 and
2 and write 4 + 2? What answer do we get? Do we get the same
answer? Yes, we do. Now I want you to take a few seconds
in your group and discuss why we get the same answer. Get
ready to share your answers.” Give the students some time to
discuss. Have them share their answers when they are done.
As the students share their answers, emphasize the fact that
it doesn't matter what order you add because you will get the
same answer.

Repeat this same process using 2 x 4 to review for
multiplication.

Then say, “The next property we are going to review is the
associative property. The associative property is similar to the
commutative property except it uses three or more numbers.”
Write 2 + 4 + 3 and 2 x 4 x 3 on the board and then say, “Let’s
start with 2 + 4 + 3. We can use parentheses to help us add
when we have more numbers.” Place parentheses around the 2
+ 4 so that it looks like (2 + 4) + 3. Most problems already have
the parentheses around them when they have three or more
numbers but it is important to help students understand that
they can use parentheses to help them out.

Say, “Remember, when using order of operations we always
do what is in parentheses first. What two numbers are in the
parentheses? 2 + 4. Let’s add those together. What do we get?
6. Good.” Write the 6 below (2 + 4). Then say, “Now that we
have added 2 and 4, we need to add 3 to our answer. Let’s add
6 + 3. What do we get? 9.”

Now say, “Let’s try this problem again, but this time we'll
move the parentheses and place them around the 4 and
3.” Place parentheses around the 4 + 3 so that the problem
now looks like 2 + (4 + 3). Ask the class, “What’s the rule
about parentheses? Good, we need to do the problem in the
parentheses first. Let’s add 4 + 3. What answer do we get? 7.”
Write the 7 below the (4 + 3).

Now ask the class, “What do we do now?” Wait for the
appropriate answer and then say, “That’s right, we need to
add 2 + 7. What do we get? 9. Did we get the same answer?
We did, didn't we? Just like the Commutative property, the
Associative property teaches us that it doesn't matter the order
in which we add three or more numbers because we will get the
same answer.”

Repeat this same exercise with 2 x 4 x 3 to review the
associative property for multiplication.

Next say, “Now that we have discussed the associative and
commutative properties, we have two more properties that we
need to talk about. These are the Identity and Zero properties
of multiplication.” Write 6 x 1 = ? on the board and ask,
“What do we get when we multiply 6 x 1?” Wait for the
students to answer. Do this a few more times with different
numbers multiplied by 1. When you have done this, ask the
class, “What do you notice about these problems?” Lead the
discussion towards the fact that any number multiplied by 1
will equal that same number. End by saying, “This is what
the Identity property teaches us. Any number multiplied by 1
equals that same number.”

“Let’s finish our review by talking about the Zero property of
multiplication.” Write 6 x 0 = ? on the board and then ask,
“Does anyone know what happens when we multiply 6 by 0?
What answer do we get? Zero, that’s right. What would happen
if I multiplied 1,000 by 0? What answer would we get? Zero
again. What about 1,000,000 x 0? Do we get zero again? We
do. This is what the Zero property of multiplication teaches us.
Any number multiplied by zero, no matter how big or small,
will always equal zero.”

Now say, “Now that we have reviewed the properties of addition
and multiplication, I am going to pass out a piece of poster
board and markers (crayons or colored pencils) to each group.
On your poster, you are going to define and give examples of
each property. You can decorate the poster however you like,
but make sure that it is your best penmanship and artwork.
You can also use your math books and math journals to help
you define the properties. If you are not sure about the wording
of your definition, raise your hand for clarification.”

Pass out the poster paper, and markers (crayons or colored
pencils), and allow the students to work on their posters. As
students work, it is important that the teacher monitors the
definitions that the students are writing.

When students are finished with their posters, allow them to
present the posters to the class and then let them decide where
they would like to hang them.

Extensions:Curriculum Extensions/Adaptations/
Integration

Advanced learners may study the history of posters and then
write a paper explaining what they found.

Learners with special needs may work cooperatively with
regular education students.

Instead of creating posters, students may develop an alternative
media source (TV commercials, postcards, radio ads) that
explain the properties.

The associative, commutative, identity, and zero properties can
be used as spelling words.

Family Connections

Students may create their own posters for their rooms or homes.

Students may create a “family” poster to share with the class.

Assessment Plan:

Use the student posters to assess student understanding of
addition and multiplication properties.

Students may develop their own property problems.

Students can conduct a survey of other classes to see if the
posters helped them remember the properties.

In this article, Millis explains the power and effectiveness of
cooperative learning. Not only is cooperative learning an effective
teaching strategy, it “promotes a shared sense of community” in the
classroom because “learning, like living, is inherently social.” As students learn to work together through cooperative learning, they
develop trust with each other and are given an opportunity to develop
self-efficacy. As teachers come to understand how to implement
cooperative learning, “student learning can be deepened, students will
enjoy attending classes, and they will come to respect and value the
contributions of their fellow classmates.”

Judy Willis states in her article that research has shown that “in
math collaboration, students learn to test one another’s conjectures
and identify valid or invalid solutions.” This happens because
cooperative learning provides students with the most opportunities to
ask questions, express ideas and opinions, and come to conclusions
that they might not otherwise have through whole group instruction.
Teachers can increase student understanding and involvement by
increasing the amount of cooperative learning in their classrooms.